Proximity-Based Point Cloud Reconstruction

Information

• Visibility: hidden
• Publication Type: PhD-Thesis
• Workgroup(s)/Project(s):
  • Rendering and Modeling
• Date: 2025
• Date (Start): September 2021
• Date (End): February 2025
• TU Wien Library: AC17518474
• Second Supervisor: Stefan Ohrhallinger
• Open Access: yes
• 1st Reviewer: Marc Alexa
• 2nd Reviewer: Leif Kobbelt
• Rigorosum: 13. February 2025
• First Supervisor: Michael Wimmer
• Pages: 141
• Keywords: point clouds, reconstruction, proximity graphs, curve reconstruction, clustering, geometry processing

Abstract

Extrapolating information from incomplete data is a key human skill, enabling us to inferpatterns and make predictions from limited observations. A prime example is our ability to perceive coherent shapes from seemingly random point sets, a key aspect of cognition.However, data reconstruction becomes challenging when no predefined rules exist, as it is unclear how to connect the data or infer patterns. In computer graphics, a major goal isto replicate this human ability by developing algorithms that can accurately reconstruct original structures or extract meaningful information from raw, disconnected data.The contributions of this thesis deal with point cloud reconstruction, leveraging proximity-based methods, with a particular focus on a specific proximity-encoding data structure -the spheres-of-influence graph (SIG). We discuss curve reconstruction, where we automate the game of connecting the dots to create contours, providing theoretical guarantees for our method. We obtain the best results compared to similar methods for manifold curves. We extend our curve reconstruction to manifolds, overcoming the challenges of moving to different domains, and extending our theoreticalguarantees. We are able to reconstruct curves from sparser inputs compared to the state-of-the-art, and we explorevarious settings in which these curves can live. We investigate the properties of the SIGas a parameter-free proximity encoding structure of three-dimensional point clouds. We introduce new spatial bounds for the SIG neighbors as a theoretical contribution. We analyze how close the encoding is to the ground truth surface compared to the commonly used kNN graphs, and we evaluate our performance in the context of normal estimationas an application. Lastly, we introduce SING – a stability-incorporated neighborhood graph, a useful tool with various applications, such as clustering, and with a strong theoretical background in topological data analysis.

Additional Files and Images

Weblinks

• Entry in reposiTUm (TU Wien Publication Database)
• DOI: 10.34726/hss.2025.128668

BibTeX

@phdthesis{marin-thesis,
  title =      "Proximity-Based Point Cloud Reconstruction",
  author =     "Diana Marin",
  year =       "2025",
  abstract =   "Extrapolating information from incomplete data is a key
               human skill, enabling us to inferpatterns and make
               predictions from limited observations. A prime example is
               our ability to perceive coherent shapes from seemingly
               random point sets, a key aspect of cognition.However, data
               reconstruction becomes challenging when no predefined rules
               exist, as it is unclear how to connect the data or infer
               patterns. In computer graphics, a major goal isto replicate
               this human ability by developing algorithms that can
               accurately reconstruct original structures or extract
               meaningful information from raw, disconnected data.The
               contributions of this thesis deal with point cloud
               reconstruction, leveraging proximity-based methods, with a
               particular focus on a specific proximity-encoding data
               structure -the spheres-of-influence graph (SIG). We discuss
               curve reconstruction, where we automate the game of
               connecting the dots to create contours, providing
               theoretical guarantees for our method. We obtain the best
               results compared to similar methods for manifold curves. We
               extend our curve reconstruction to manifolds, overcoming the
               challenges of moving to different domains, and extending our
               theoreticalguarantees. We are able to reconstruct curves
               from sparser inputs compared to the state-of-the-art, and we
               explorevarious settings in which these curves can live. We
               investigate the properties of the SIGas a parameter-free
               proximity encoding structure of three-dimensional point
               clouds. We introduce new spatial bounds for the SIG
               neighbors as a theoretical contribution. We analyze how
               close the encoding is to the ground truth surface compared
               to the commonly used kNN graphs, and we evaluate our
               performance in the context of normal estimationas an
               application. Lastly, we introduce SING – a
               stability-incorporated neighborhood graph, a useful tool
               with various applications, such as clustering, and with a
               strong theoretical background in topological data analysis.",
  pages =      "141",
  address =    "Favoritenstrasse 9-11/E193-02, A-1040 Vienna, Austria",
  school =     "Research Unit of Computer Graphics, Institute of Visual
               Computing and Human-Centered Technology, Faculty of
               Informatics, TU Wien ",
  keywords =   "point clouds, reconstruction, proximity graphs, curve
               reconstruction, clustering, geometry processing",
  URL =        "https://www.cg.tuwien.ac.at/research/publications/2025/marin-thesis/",
}